One member of Fathom’s staff yesterday found his journey into work delayed by a swan. The offending fowl had found its way onto the train track and, in the high-and-mighty, supercilious manner of swans the world over, refused to move. With apologies to Her Majesty, it’s enough to make one reconsider the relative merits of roast swan, compared to turkey or chicken, or other more ‘normal’ poultry options.

This being the tenth anniversary of the start of the great financial crisis, swans are much in our minds – particularly black swans, made famous by Nassim Taleb’s work that urged us all to consider low-probability, high-impact events more rigorously than we previously had. That lesson has stuck, and risk analysis, particularly in relation to extreme events, has been a feature of much economic research ever since. In our defence, this was always Fathom’s approach – it is not much use telling our clients that everything will probably proceed normally, since they already know that. Much more useful to identify the ways in which things might go awry, either on the upside or the downside.

Extreme events should be considered as a part of normal risk management. It should be normal to consider the extremes. The extremes are part of the normal. How big a part, that’s the question.

When we were children, my sister and I played a game in which we categorised the people we knew – friends, enemies, relations, teachers etc. – according to where they stood relative to what we perceived as ‘normal’. Most people were ‘normals’. Katy wears pastels, likes David Cassidy, regularly gets marked ‘B’ for her homework, eats white-sliced-bread sandwiches with ham for lunch, which she brings to school in a red Tupperware box, loves horses although she has never ridden one, has a Cindy doll and a dog named Bobby, and enjoys watching Top of the Pops.

By our lights at the time, normals were boring people: not like us. We were un-normal, which was the correct thing to be. Un-normals were cool, and did things differently. Of course, there has always been a counterculture, connected symbiotically to the mainstream. In the 1960s we would have been called hippies. In the 1970s it was punk. In the 1980s it morphed into ‘new wave’ and then ‘alternative’. We would have rejected all of those labels, but in truth that’s what we were.

There were two other principal categories in our game: so-normals and eccentrics. So-normals were, well, so normal that they stopped being normal. They went right through normal and came out the other side. Outstandingly, egregiously normal. You know the type, right? Neurotic about their need to be perceived as normal. Trying so hard to be normal that people noticed it, which of course is the last thing they want. Which would cause them to redouble their efforts to appear normal. As Joseph Heller wrote in Catch-22:

“Some people are born mediocre, some people achieve mediocrity, and some people have mediocrity thrust upon them. With Major Major it was all three.”

Major Major was so-normal.

Eccentrics defied classification. Unlike un-normals such as ourselves, eccentrics had no sense of what was normal or otherwise – they just did their thing, believing it to be normal. Wrongly. Eccentrics were funny, but weird.

The game was fun, and I forgive myself the cruelty that it involved because we didn’t tell people about it – we never used it to hurt them. In hindsight, it was a defensive game: we felt that we came from an unusual family in many respects, and devised a way of making sense of that for ourselves.

The term ‘normal’ often has an overtone of cruelty. It is often used (as it was in our game) to identify those who are like us in some way and, more particularly, those who are not like us. And then it can be taken further, to apply peer pressure to the outsiders to get them to become more like us, or to punish them for not being so in the first place.

Normal is also strange – it denotes a norm that almost nobody actually conforms to. As the decades have raced by, it has become clear to me that the set of normal people is really very small. Everyone has an unusual family, not just me.

As the band Arcade Fire have asked:

“Is anyone as strange as a normal person?

Is anyone as cruel as a normal person?”

However, in a statistical or an economic sense, this way of thinking, which allows the weaponisation of the term ‘normal’, is completely wrong. ‘Normal’, for economists, is not a feature of individuals but of distributions. It doesn’t make sense to ask whether any individual is normal or otherwise. But it does make sense to ask that question of the whole distribution of individuals.

All the categories in our game – normal, un-normal, so-normal and even eccentric – could in principle be encompassed within the statistical meaning of ‘normal’, in the sense of being drawn from a normal distribution: a bell-curve.

The received economic wisdom states that all that humans do, all that we are, all that we believe, is normal in this sense. The tails of the distribution are just as much part of the ‘normal’ as the mode. ‘Normal’, in its statistical sense, cannot be used as a weapon with which to demonise minorities of any sort: minorities are part of the normal.

All of this is normal.

So what?

One of the other supposed lessons from Taleb’s work was that perhaps we should consider other distributions than the normal when thinking about the likelihood of extreme events – distributions with ‘fatter tails’ (which essentially attribute a higher likelihood to extreme events than a normal distribution would).

Famously, ahead of the great financial crisis, the thought process that concluded that it was sensible to give an AAA rating to structured products that contained sub-prime (or even NINJA) mortgages was based on an observation that national house prices in the US had never fallen, so the risk of such a fall could safely be regarded as negligible. Consequently, as long as the structured product was ‘diverse’ in the sense of including a spread of housing across the country, the risk of an across-the-board fall in the value of the underlying asset could be treated as negligible. Some may fall, but others must rise, because otherwise the stylised fact (national house prices never fall) could not be true.

But that conclusion was always flawed. The fact that national house prices had never fallen in the US did not imply that the risk of a fall was negligible – national house prices had frequently fallen in other countries. The US offered a small sample of that much wider population of house price movements. However, neither the US nor the cross-country data are distributed normally.

In the US alone, using Federal Housing Finance Agency (FHFA) data encompassing the period of the great financial crisis, we can strongly reject the hypothesis that the distribution of national house price movements is normal. And the same is true using data across a pool of major economies including the US for which consistent house price series exist. Both distributions exhibit excess kurtosis relative to the normal distribution. And the same is true even if we cut the data before the financial crisis.

However, tests of normality like the Jarque-Bera test above are notoriously weak when the sample is small, where ‘small’ means fewer than 2000 observations. Even across countries, the sample we have looked at is still small in that sense. We cannot decisively reject the hypothesis that the distribution of house price movements across countries is drawn from a normal distribution without a much larger sample. But we don’t have such a sample so, for now, Taleb’s point stands: the chances of extreme events occurring in the housing market are greater than we would find them to be if we assumed a normal distribution with a variance consistent with the data.

It’s unlikely that house price growth is distributed normally. Just like individuals – nobody I’ve met comes from a normal family. I suppose such families exist, but they are few and far between. Quoting Arcade Fire again: